The question without the accompanying diagram could also mean to roll the small circle within the larger one. If this is done you actually lose a rotation. The answer then is 3!
The easiest way to calculate the rotations is to use the path taken by the centre of the small circle.
If r[1] = radius of small circle; r[2] = radius of path outside and r[3] = radius of path inside the large circle then:-
Rotations outside = (2 x pi x r[2])/(2 x pi x r[1]) = (2 x pi x 5)/(2 x pi x 1) = 5/1 = 5.
Rotations inside = (2 x pi x r[3])/(2 x pi x r[1]) = (2 x pi x 3)/(2 x pi x 1) = 3/1 = 3.

K. Selby

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